Chi-square test
A chi-square test is any statistical hypothesis test in which the test statistic has a chi-square distribution if the null hypothesis is true. These include: * Pearson's chi-square test * Yates' chi-square test also known as Yates' correction for continuity * Mantel-Haenszel chi-square test * linear-by-linear association chi-square test * Chi-square goodness-of-fit test The most common form of the test statistic is: : \chi^2=\sum\frac{(\mathrm{observed}-\mathrm{expected})^2}{\mathrm{expected}}, where the word "expected" often does not denote an expected value, but an observable estimate of an expected value. However, likelihood ratio tests do not have this form. The chi-square test is a statistical tool to separate real effects from random variation. It can be used on data that is: # randomly drawn from the population # reported in raw counts of frequency (not percentages or rates) # measured variables must be independent # values on independent and dependent variables must be mutually exclusive # observed frequencies cannot be too small The chi-square test determines the probability of obtaining the observed results by chance, under a specific hypothesis. It tests independence as well as goodness of fit for a set of data. See also * General likelihood-ratio tests, which are approximately chi-square tests. * McNemar's test, related to a chi-square test * The Wald test, which can be evaluated against a chi-square distribution p value (e.g., p'' = 0.05). It is an indication of the likelihood of obtaining a result (0.05 = 5%). As such, it is relatively uninformative. A more helpful accompanying statistic is phi (or Cramer's phi, or Cramer's V).Aaron, B., Kromrey, J. D., & Ferron, J. M. (1998, November). Equating r-based and d-based effect-size indices: Problems with a commonly recommended formula. Paper presented at the annual meeting of the Florida Educational Research Association, Orlando, FL. (ERIC Document Reproduction Service No. ED433353) Phi is a measure of association that reports a value for the correlation between the two dichotomous variables compared in a chi-square test (2 × 2). This value gives you an indication of the extent of the relationship between the two variables. Cramer's phi can be used for even larger comparisons. It is a more meaningful measure of the practical significance of the chi-square test and is reported as the effect size. Chi-square test for contingency table A chi-square test may be applied on a contingency table for testing a null hypothesis of independence of rows and columns. Example A fair coin is one where heads and tails are equally likely to turn up after it is flipped. You are given a coin and asked to test if it is fair. After 100 trials, heads turn up 53 times and tails result 47 times. Here is a Chi-square analysis, where the null hypothesis is that the coin is fair: Since there is one(1) degree of freedom, ''p = 0.5485. There is thus a 54.85% chance of seeing this data if the coin is fair, which is not considered statistically significant evidence that the coin is NOT fair. See also * General likelihood-ratio tests, which are approximately chi-square tests * McNemar's test, related to a chi-square test * Statistical signifiance * The Wald test, which can be evaluated against a chi-square distribution External links *Chi-Square Calculator from GraphPad *Vassar College's 2x2 Chi-Square with Expected Values References Category:Statistical tests Category:Nonparametric statistical tests